Simplify the following expression: $z = \dfrac{40k - 8}{-36k - 32}$ You can assume $k \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $40k - 8 = (2\cdot2\cdot2\cdot5 \cdot k) - (2\cdot2\cdot2)$ The denominator can be factored: $-36k - 32 = - (2\cdot2\cdot3\cdot3 \cdot k) - (2\cdot2\cdot2\cdot2\cdot2)$ The greatest common factor of all the terms is $4$ Factoring out $4$ gives us: $z = \dfrac{(4)(10k - 2)}{(4)(-9k - 8)}$ Dividing both the numerator and denominator by $4$ gives: $z = \dfrac{10k - 2}{-9k - 8}$